Properties

Label 6017.2.a.c.1.3
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.73187 q^{2}\) \(-0.157601 q^{3}\) \(+5.46313 q^{4}\) \(+2.56928 q^{5}\) \(+0.430546 q^{6}\) \(-5.24072 q^{7}\) \(-9.46082 q^{8}\) \(-2.97516 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.73187 q^{2}\) \(-0.157601 q^{3}\) \(+5.46313 q^{4}\) \(+2.56928 q^{5}\) \(+0.430546 q^{6}\) \(-5.24072 q^{7}\) \(-9.46082 q^{8}\) \(-2.97516 q^{9}\) \(-7.01894 q^{10}\) \(+1.00000 q^{11}\) \(-0.860994 q^{12}\) \(-5.86953 q^{13}\) \(+14.3170 q^{14}\) \(-0.404921 q^{15}\) \(+14.9195 q^{16}\) \(+0.0371539 q^{17}\) \(+8.12776 q^{18}\) \(+7.34848 q^{19}\) \(+14.0363 q^{20}\) \(+0.825943 q^{21}\) \(-2.73187 q^{22}\) \(-3.50507 q^{23}\) \(+1.49103 q^{24}\) \(+1.60119 q^{25}\) \(+16.0348 q^{26}\) \(+0.941692 q^{27}\) \(-28.6307 q^{28}\) \(+0.837837 q^{29}\) \(+1.10619 q^{30}\) \(+1.36511 q^{31}\) \(-21.8365 q^{32}\) \(-0.157601 q^{33}\) \(-0.101500 q^{34}\) \(-13.4649 q^{35}\) \(-16.2537 q^{36}\) \(+5.04931 q^{37}\) \(-20.0751 q^{38}\) \(+0.925043 q^{39}\) \(-24.3075 q^{40}\) \(-2.95624 q^{41}\) \(-2.25637 q^{42}\) \(+5.22482 q^{43}\) \(+5.46313 q^{44}\) \(-7.64402 q^{45}\) \(+9.57541 q^{46}\) \(+6.75107 q^{47}\) \(-2.35133 q^{48}\) \(+20.4652 q^{49}\) \(-4.37424 q^{50}\) \(-0.00585550 q^{51}\) \(-32.0660 q^{52}\) \(+4.83982 q^{53}\) \(-2.57258 q^{54}\) \(+2.56928 q^{55}\) \(+49.5815 q^{56}\) \(-1.15813 q^{57}\) \(-2.28886 q^{58}\) \(+6.77803 q^{59}\) \(-2.21213 q^{60}\) \(-4.16001 q^{61}\) \(-3.72931 q^{62}\) \(+15.5920 q^{63}\) \(+29.8156 q^{64}\) \(-15.0804 q^{65}\) \(+0.430546 q^{66}\) \(+8.81152 q^{67}\) \(+0.202977 q^{68}\) \(+0.552403 q^{69}\) \(+36.7843 q^{70}\) \(-10.2332 q^{71}\) \(+28.1475 q^{72}\) \(+0.960007 q^{73}\) \(-13.7941 q^{74}\) \(-0.252349 q^{75}\) \(+40.1457 q^{76}\) \(-5.24072 q^{77}\) \(-2.52710 q^{78}\) \(-2.38437 q^{79}\) \(+38.3323 q^{80}\) \(+8.77707 q^{81}\) \(+8.07608 q^{82}\) \(+6.92736 q^{83}\) \(+4.51223 q^{84}\) \(+0.0954587 q^{85}\) \(-14.2735 q^{86}\) \(-0.132044 q^{87}\) \(-9.46082 q^{88}\) \(+3.29656 q^{89}\) \(+20.8825 q^{90}\) \(+30.7606 q^{91}\) \(-19.1486 q^{92}\) \(-0.215143 q^{93}\) \(-18.4430 q^{94}\) \(+18.8803 q^{95}\) \(+3.44146 q^{96}\) \(+10.2366 q^{97}\) \(-55.9082 q^{98}\) \(-2.97516 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73187 −1.93173 −0.965863 0.259055i \(-0.916589\pi\)
−0.965863 + 0.259055i \(0.916589\pi\)
\(3\) −0.157601 −0.0909910 −0.0454955 0.998965i \(-0.514487\pi\)
−0.0454955 + 0.998965i \(0.514487\pi\)
\(4\) 5.46313 2.73156
\(5\) 2.56928 1.14902 0.574508 0.818499i \(-0.305193\pi\)
0.574508 + 0.818499i \(0.305193\pi\)
\(6\) 0.430546 0.175770
\(7\) −5.24072 −1.98081 −0.990403 0.138208i \(-0.955866\pi\)
−0.990403 + 0.138208i \(0.955866\pi\)
\(8\) −9.46082 −3.34490
\(9\) −2.97516 −0.991721
\(10\) −7.01894 −2.21958
\(11\) 1.00000 0.301511
\(12\) −0.860994 −0.248548
\(13\) −5.86953 −1.62791 −0.813957 0.580925i \(-0.802691\pi\)
−0.813957 + 0.580925i \(0.802691\pi\)
\(14\) 14.3170 3.82637
\(15\) −0.404921 −0.104550
\(16\) 14.9195 3.72987
\(17\) 0.0371539 0.00901115 0.00450557 0.999990i \(-0.498566\pi\)
0.00450557 + 0.999990i \(0.498566\pi\)
\(18\) 8.12776 1.91573
\(19\) 7.34848 1.68586 0.842929 0.538025i \(-0.180829\pi\)
0.842929 + 0.538025i \(0.180829\pi\)
\(20\) 14.0363 3.13861
\(21\) 0.825943 0.180236
\(22\) −2.73187 −0.582437
\(23\) −3.50507 −0.730858 −0.365429 0.930839i \(-0.619078\pi\)
−0.365429 + 0.930839i \(0.619078\pi\)
\(24\) 1.49103 0.304356
\(25\) 1.60119 0.320238
\(26\) 16.0348 3.14468
\(27\) 0.941692 0.181229
\(28\) −28.6307 −5.41070
\(29\) 0.837837 0.155582 0.0777912 0.996970i \(-0.475213\pi\)
0.0777912 + 0.996970i \(0.475213\pi\)
\(30\) 1.10619 0.201962
\(31\) 1.36511 0.245181 0.122591 0.992457i \(-0.460880\pi\)
0.122591 + 0.992457i \(0.460880\pi\)
\(32\) −21.8365 −3.86019
\(33\) −0.157601 −0.0274348
\(34\) −0.101500 −0.0174071
\(35\) −13.4649 −2.27598
\(36\) −16.2537 −2.70895
\(37\) 5.04931 0.830102 0.415051 0.909798i \(-0.363764\pi\)
0.415051 + 0.909798i \(0.363764\pi\)
\(38\) −20.0751 −3.25661
\(39\) 0.925043 0.148125
\(40\) −24.3075 −3.84335
\(41\) −2.95624 −0.461688 −0.230844 0.972991i \(-0.574149\pi\)
−0.230844 + 0.972991i \(0.574149\pi\)
\(42\) −2.25637 −0.348166
\(43\) 5.22482 0.796777 0.398389 0.917217i \(-0.369570\pi\)
0.398389 + 0.917217i \(0.369570\pi\)
\(44\) 5.46313 0.823597
\(45\) −7.64402 −1.13950
\(46\) 9.57541 1.41182
\(47\) 6.75107 0.984744 0.492372 0.870385i \(-0.336130\pi\)
0.492372 + 0.870385i \(0.336130\pi\)
\(48\) −2.35133 −0.339385
\(49\) 20.4652 2.92359
\(50\) −4.37424 −0.618611
\(51\) −0.00585550 −0.000819933 0
\(52\) −32.0660 −4.44675
\(53\) 4.83982 0.664800 0.332400 0.943138i \(-0.392142\pi\)
0.332400 + 0.943138i \(0.392142\pi\)
\(54\) −2.57258 −0.350084
\(55\) 2.56928 0.346441
\(56\) 49.5815 6.62561
\(57\) −1.15813 −0.153398
\(58\) −2.28886 −0.300542
\(59\) 6.77803 0.882425 0.441212 0.897403i \(-0.354549\pi\)
0.441212 + 0.897403i \(0.354549\pi\)
\(60\) −2.21213 −0.285585
\(61\) −4.16001 −0.532635 −0.266317 0.963885i \(-0.585807\pi\)
−0.266317 + 0.963885i \(0.585807\pi\)
\(62\) −3.72931 −0.473623
\(63\) 15.5920 1.96441
\(64\) 29.8156 3.72695
\(65\) −15.0804 −1.87050
\(66\) 0.430546 0.0529965
\(67\) 8.81152 1.07650 0.538249 0.842786i \(-0.319086\pi\)
0.538249 + 0.842786i \(0.319086\pi\)
\(68\) 0.202977 0.0246145
\(69\) 0.552403 0.0665015
\(70\) 36.7843 4.39656
\(71\) −10.2332 −1.21446 −0.607230 0.794526i \(-0.707719\pi\)
−0.607230 + 0.794526i \(0.707719\pi\)
\(72\) 28.1475 3.31721
\(73\) 0.960007 0.112360 0.0561801 0.998421i \(-0.482108\pi\)
0.0561801 + 0.998421i \(0.482108\pi\)
\(74\) −13.7941 −1.60353
\(75\) −0.252349 −0.0291387
\(76\) 40.1457 4.60503
\(77\) −5.24072 −0.597236
\(78\) −2.52710 −0.286138
\(79\) −2.38437 −0.268263 −0.134131 0.990964i \(-0.542824\pi\)
−0.134131 + 0.990964i \(0.542824\pi\)
\(80\) 38.3323 4.28568
\(81\) 8.77707 0.975230
\(82\) 8.07608 0.891854
\(83\) 6.92736 0.760377 0.380188 0.924909i \(-0.375859\pi\)
0.380188 + 0.924909i \(0.375859\pi\)
\(84\) 4.51223 0.492325
\(85\) 0.0954587 0.0103540
\(86\) −14.2735 −1.53916
\(87\) −0.132044 −0.0141566
\(88\) −9.46082 −1.00853
\(89\) 3.29656 0.349434 0.174717 0.984619i \(-0.444099\pi\)
0.174717 + 0.984619i \(0.444099\pi\)
\(90\) 20.8825 2.20121
\(91\) 30.7606 3.22458
\(92\) −19.1486 −1.99638
\(93\) −0.215143 −0.0223093
\(94\) −18.4430 −1.90226
\(95\) 18.8803 1.93708
\(96\) 3.44146 0.351242
\(97\) 10.2366 1.03937 0.519683 0.854359i \(-0.326050\pi\)
0.519683 + 0.854359i \(0.326050\pi\)
\(98\) −55.9082 −5.64758
\(99\) −2.97516 −0.299015
\(100\) 8.74749 0.874749
\(101\) −1.42485 −0.141778 −0.0708889 0.997484i \(-0.522584\pi\)
−0.0708889 + 0.997484i \(0.522584\pi\)
\(102\) 0.0159965 0.00158389
\(103\) −10.0955 −0.994739 −0.497370 0.867539i \(-0.665701\pi\)
−0.497370 + 0.867539i \(0.665701\pi\)
\(104\) 55.5305 5.44521
\(105\) 2.12208 0.207094
\(106\) −13.2218 −1.28421
\(107\) 9.55763 0.923971 0.461985 0.886888i \(-0.347137\pi\)
0.461985 + 0.886888i \(0.347137\pi\)
\(108\) 5.14458 0.495037
\(109\) 2.36305 0.226339 0.113169 0.993576i \(-0.463900\pi\)
0.113169 + 0.993576i \(0.463900\pi\)
\(110\) −7.01894 −0.669230
\(111\) −0.795777 −0.0755318
\(112\) −78.1889 −7.38816
\(113\) −11.7275 −1.10323 −0.551613 0.834100i \(-0.685988\pi\)
−0.551613 + 0.834100i \(0.685988\pi\)
\(114\) 3.16386 0.296323
\(115\) −9.00550 −0.839767
\(116\) 4.57721 0.424983
\(117\) 17.4628 1.61444
\(118\) −18.5167 −1.70460
\(119\) −0.194713 −0.0178493
\(120\) 3.83088 0.349710
\(121\) 1.00000 0.0909091
\(122\) 11.3646 1.02890
\(123\) 0.465907 0.0420094
\(124\) 7.45777 0.669728
\(125\) −8.73249 −0.781058
\(126\) −42.5953 −3.79469
\(127\) −15.6522 −1.38891 −0.694453 0.719538i \(-0.744354\pi\)
−0.694453 + 0.719538i \(0.744354\pi\)
\(128\) −37.7793 −3.33925
\(129\) −0.823437 −0.0724996
\(130\) 41.1978 3.61329
\(131\) −5.17965 −0.452548 −0.226274 0.974064i \(-0.572654\pi\)
−0.226274 + 0.974064i \(0.572654\pi\)
\(132\) −0.860994 −0.0749399
\(133\) −38.5114 −3.33936
\(134\) −24.0719 −2.07950
\(135\) 2.41947 0.208235
\(136\) −0.351506 −0.0301414
\(137\) −12.0733 −1.03149 −0.515746 0.856741i \(-0.672485\pi\)
−0.515746 + 0.856741i \(0.672485\pi\)
\(138\) −1.50909 −0.128463
\(139\) 20.7489 1.75990 0.879951 0.475065i \(-0.157576\pi\)
0.879951 + 0.475065i \(0.157576\pi\)
\(140\) −73.5603 −6.21698
\(141\) −1.06397 −0.0896029
\(142\) 27.9559 2.34600
\(143\) −5.86953 −0.490834
\(144\) −44.3879 −3.69899
\(145\) 2.15263 0.178767
\(146\) −2.62262 −0.217049
\(147\) −3.22533 −0.266021
\(148\) 27.5850 2.26748
\(149\) −5.61262 −0.459804 −0.229902 0.973214i \(-0.573841\pi\)
−0.229902 + 0.973214i \(0.573841\pi\)
\(150\) 0.689385 0.0562880
\(151\) −5.89696 −0.479888 −0.239944 0.970787i \(-0.577129\pi\)
−0.239944 + 0.970787i \(0.577129\pi\)
\(152\) −69.5227 −5.63903
\(153\) −0.110539 −0.00893654
\(154\) 14.3170 1.15370
\(155\) 3.50735 0.281717
\(156\) 5.05363 0.404614
\(157\) −24.0535 −1.91968 −0.959840 0.280549i \(-0.909483\pi\)
−0.959840 + 0.280549i \(0.909483\pi\)
\(158\) 6.51380 0.518210
\(159\) −0.762760 −0.0604908
\(160\) −56.1041 −4.43542
\(161\) 18.3691 1.44769
\(162\) −23.9778 −1.88388
\(163\) −16.5039 −1.29268 −0.646341 0.763049i \(-0.723702\pi\)
−0.646341 + 0.763049i \(0.723702\pi\)
\(164\) −16.1503 −1.26113
\(165\) −0.404921 −0.0315230
\(166\) −18.9247 −1.46884
\(167\) −14.0421 −1.08661 −0.543306 0.839534i \(-0.682828\pi\)
−0.543306 + 0.839534i \(0.682828\pi\)
\(168\) −7.81410 −0.602871
\(169\) 21.4513 1.65010
\(170\) −0.260781 −0.0200010
\(171\) −21.8629 −1.67190
\(172\) 28.5438 2.17645
\(173\) 22.7459 1.72934 0.864668 0.502343i \(-0.167528\pi\)
0.864668 + 0.502343i \(0.167528\pi\)
\(174\) 0.360727 0.0273466
\(175\) −8.39138 −0.634329
\(176\) 14.9195 1.12460
\(177\) −1.06823 −0.0802927
\(178\) −9.00577 −0.675011
\(179\) −7.90539 −0.590876 −0.295438 0.955362i \(-0.595466\pi\)
−0.295438 + 0.955362i \(0.595466\pi\)
\(180\) −41.7602 −3.11262
\(181\) −24.4062 −1.81410 −0.907048 0.421027i \(-0.861670\pi\)
−0.907048 + 0.421027i \(0.861670\pi\)
\(182\) −84.0339 −6.22901
\(183\) 0.655622 0.0484650
\(184\) 33.1608 2.44465
\(185\) 12.9731 0.953800
\(186\) 0.587743 0.0430954
\(187\) 0.0371539 0.00271696
\(188\) 36.8819 2.68989
\(189\) −4.93514 −0.358979
\(190\) −51.5786 −3.74190
\(191\) 3.82760 0.276956 0.138478 0.990366i \(-0.455779\pi\)
0.138478 + 0.990366i \(0.455779\pi\)
\(192\) −4.69896 −0.339119
\(193\) 3.80124 0.273619 0.136810 0.990597i \(-0.456315\pi\)
0.136810 + 0.990597i \(0.456315\pi\)
\(194\) −27.9650 −2.00777
\(195\) 2.37669 0.170199
\(196\) 111.804 7.98598
\(197\) 14.8583 1.05861 0.529303 0.848433i \(-0.322453\pi\)
0.529303 + 0.848433i \(0.322453\pi\)
\(198\) 8.12776 0.577615
\(199\) −23.5277 −1.66783 −0.833917 0.551890i \(-0.813907\pi\)
−0.833917 + 0.551890i \(0.813907\pi\)
\(200\) −15.1485 −1.07116
\(201\) −1.38870 −0.0979516
\(202\) 3.89250 0.273876
\(203\) −4.39087 −0.308179
\(204\) −0.0319893 −0.00223970
\(205\) −7.59541 −0.530486
\(206\) 27.5796 1.92156
\(207\) 10.4282 0.724807
\(208\) −87.5703 −6.07191
\(209\) 7.34848 0.508305
\(210\) −5.79724 −0.400048
\(211\) −5.00325 −0.344438 −0.172219 0.985059i \(-0.555094\pi\)
−0.172219 + 0.985059i \(0.555094\pi\)
\(212\) 26.4405 1.81594
\(213\) 1.61277 0.110505
\(214\) −26.1102 −1.78486
\(215\) 13.4240 0.915510
\(216\) −8.90917 −0.606192
\(217\) −7.15417 −0.485657
\(218\) −6.45555 −0.437225
\(219\) −0.151298 −0.0102238
\(220\) 14.0363 0.946326
\(221\) −0.218076 −0.0146694
\(222\) 2.17396 0.145907
\(223\) −26.3785 −1.76643 −0.883217 0.468965i \(-0.844627\pi\)
−0.883217 + 0.468965i \(0.844627\pi\)
\(224\) 114.439 7.64628
\(225\) −4.76379 −0.317586
\(226\) 32.0379 2.13113
\(227\) −26.5402 −1.76153 −0.880766 0.473552i \(-0.842972\pi\)
−0.880766 + 0.473552i \(0.842972\pi\)
\(228\) −6.32700 −0.419016
\(229\) 11.8693 0.784343 0.392172 0.919892i \(-0.371724\pi\)
0.392172 + 0.919892i \(0.371724\pi\)
\(230\) 24.6019 1.62220
\(231\) 0.825943 0.0543431
\(232\) −7.92662 −0.520408
\(233\) 1.28760 0.0843536 0.0421768 0.999110i \(-0.486571\pi\)
0.0421768 + 0.999110i \(0.486571\pi\)
\(234\) −47.7061 −3.11865
\(235\) 17.3454 1.13149
\(236\) 37.0293 2.41040
\(237\) 0.375779 0.0244095
\(238\) 0.531932 0.0344800
\(239\) −20.7077 −1.33947 −0.669734 0.742601i \(-0.733592\pi\)
−0.669734 + 0.742601i \(0.733592\pi\)
\(240\) −6.04121 −0.389959
\(241\) −12.6613 −0.815585 −0.407792 0.913075i \(-0.633701\pi\)
−0.407792 + 0.913075i \(0.633701\pi\)
\(242\) −2.73187 −0.175611
\(243\) −4.20835 −0.269966
\(244\) −22.7267 −1.45493
\(245\) 52.5807 3.35926
\(246\) −1.27280 −0.0811506
\(247\) −43.1321 −2.74443
\(248\) −12.9151 −0.820108
\(249\) −1.09176 −0.0691875
\(250\) 23.8561 1.50879
\(251\) 10.8385 0.684121 0.342060 0.939678i \(-0.388875\pi\)
0.342060 + 0.939678i \(0.388875\pi\)
\(252\) 85.1810 5.36590
\(253\) −3.50507 −0.220362
\(254\) 42.7598 2.68299
\(255\) −0.0150444 −0.000942117 0
\(256\) 43.5771 2.72357
\(257\) 27.1587 1.69411 0.847057 0.531502i \(-0.178372\pi\)
0.847057 + 0.531502i \(0.178372\pi\)
\(258\) 2.24952 0.140049
\(259\) −26.4620 −1.64427
\(260\) −82.3864 −5.10938
\(261\) −2.49270 −0.154294
\(262\) 14.1501 0.874198
\(263\) 23.4738 1.44745 0.723727 0.690086i \(-0.242427\pi\)
0.723727 + 0.690086i \(0.242427\pi\)
\(264\) 1.49103 0.0917668
\(265\) 12.4348 0.763866
\(266\) 105.208 6.45072
\(267\) −0.519541 −0.0317954
\(268\) 48.1384 2.94052
\(269\) 15.0039 0.914807 0.457403 0.889259i \(-0.348780\pi\)
0.457403 + 0.889259i \(0.348780\pi\)
\(270\) −6.60968 −0.402252
\(271\) −11.2002 −0.680363 −0.340182 0.940360i \(-0.610489\pi\)
−0.340182 + 0.940360i \(0.610489\pi\)
\(272\) 0.554318 0.0336104
\(273\) −4.84789 −0.293408
\(274\) 32.9827 1.99256
\(275\) 1.60119 0.0965553
\(276\) 3.01785 0.181653
\(277\) −26.1664 −1.57219 −0.786095 0.618106i \(-0.787900\pi\)
−0.786095 + 0.618106i \(0.787900\pi\)
\(278\) −56.6834 −3.39965
\(279\) −4.06143 −0.243151
\(280\) 127.389 7.61293
\(281\) 26.2595 1.56651 0.783255 0.621701i \(-0.213558\pi\)
0.783255 + 0.621701i \(0.213558\pi\)
\(282\) 2.90664 0.173088
\(283\) −24.5286 −1.45807 −0.729036 0.684475i \(-0.760031\pi\)
−0.729036 + 0.684475i \(0.760031\pi\)
\(284\) −55.9054 −3.31738
\(285\) −2.97555 −0.176257
\(286\) 16.0348 0.948157
\(287\) 15.4928 0.914514
\(288\) 64.9671 3.82823
\(289\) −16.9986 −0.999919
\(290\) −5.88072 −0.345328
\(291\) −1.61329 −0.0945730
\(292\) 5.24464 0.306919
\(293\) 23.6369 1.38088 0.690441 0.723389i \(-0.257416\pi\)
0.690441 + 0.723389i \(0.257416\pi\)
\(294\) 8.81119 0.513879
\(295\) 17.4147 1.01392
\(296\) −47.7706 −2.77661
\(297\) 0.941692 0.0546425
\(298\) 15.3330 0.888214
\(299\) 20.5731 1.18977
\(300\) −1.37861 −0.0795943
\(301\) −27.3818 −1.57826
\(302\) 16.1098 0.927012
\(303\) 0.224558 0.0129005
\(304\) 109.636 6.28804
\(305\) −10.6882 −0.612006
\(306\) 0.301978 0.0172629
\(307\) 17.1691 0.979891 0.489945 0.871753i \(-0.337017\pi\)
0.489945 + 0.871753i \(0.337017\pi\)
\(308\) −28.6307 −1.63139
\(309\) 1.59106 0.0905123
\(310\) −9.58163 −0.544200
\(311\) −18.5309 −1.05079 −0.525395 0.850858i \(-0.676083\pi\)
−0.525395 + 0.850858i \(0.676083\pi\)
\(312\) −8.75167 −0.495466
\(313\) −24.2433 −1.37031 −0.685157 0.728395i \(-0.740266\pi\)
−0.685157 + 0.728395i \(0.740266\pi\)
\(314\) 65.7111 3.70829
\(315\) 40.0602 2.25713
\(316\) −13.0261 −0.732776
\(317\) −0.180553 −0.0101409 −0.00507043 0.999987i \(-0.501614\pi\)
−0.00507043 + 0.999987i \(0.501614\pi\)
\(318\) 2.08376 0.116852
\(319\) 0.837837 0.0469098
\(320\) 76.6045 4.28232
\(321\) −1.50629 −0.0840730
\(322\) −50.1820 −2.79654
\(323\) 0.273025 0.0151915
\(324\) 47.9503 2.66390
\(325\) −9.39822 −0.521319
\(326\) 45.0864 2.49711
\(327\) −0.372419 −0.0205948
\(328\) 27.9685 1.54430
\(329\) −35.3805 −1.95059
\(330\) 1.10619 0.0608939
\(331\) 2.08357 0.114523 0.0572617 0.998359i \(-0.481763\pi\)
0.0572617 + 0.998359i \(0.481763\pi\)
\(332\) 37.8451 2.07702
\(333\) −15.0225 −0.823229
\(334\) 38.3613 2.09904
\(335\) 22.6392 1.23691
\(336\) 12.3227 0.672256
\(337\) 5.70795 0.310932 0.155466 0.987841i \(-0.450312\pi\)
0.155466 + 0.987841i \(0.450312\pi\)
\(338\) −58.6023 −3.18755
\(339\) 1.84826 0.100384
\(340\) 0.521503 0.0282825
\(341\) 1.36511 0.0739249
\(342\) 59.7267 3.22965
\(343\) −70.5672 −3.81027
\(344\) −49.4311 −2.66514
\(345\) 1.41928 0.0764113
\(346\) −62.1388 −3.34060
\(347\) −29.2406 −1.56972 −0.784859 0.619675i \(-0.787264\pi\)
−0.784859 + 0.619675i \(0.787264\pi\)
\(348\) −0.721372 −0.0386696
\(349\) −5.34262 −0.285984 −0.142992 0.989724i \(-0.545672\pi\)
−0.142992 + 0.989724i \(0.545672\pi\)
\(350\) 22.9242 1.22535
\(351\) −5.52728 −0.295025
\(352\) −21.8365 −1.16389
\(353\) −15.7190 −0.836638 −0.418319 0.908300i \(-0.637381\pi\)
−0.418319 + 0.908300i \(0.637381\pi\)
\(354\) 2.91825 0.155103
\(355\) −26.2920 −1.39543
\(356\) 18.0095 0.954502
\(357\) 0.0306870 0.00162413
\(358\) 21.5965 1.14141
\(359\) −0.343054 −0.0181057 −0.00905284 0.999959i \(-0.502882\pi\)
−0.00905284 + 0.999959i \(0.502882\pi\)
\(360\) 72.3186 3.81153
\(361\) 35.0002 1.84212
\(362\) 66.6745 3.50434
\(363\) −0.157601 −0.00827191
\(364\) 168.049 8.80815
\(365\) 2.46652 0.129104
\(366\) −1.79108 −0.0936210
\(367\) 20.0334 1.04574 0.522868 0.852414i \(-0.324862\pi\)
0.522868 + 0.852414i \(0.324862\pi\)
\(368\) −52.2939 −2.72601
\(369\) 8.79530 0.457865
\(370\) −35.4408 −1.84248
\(371\) −25.3641 −1.31684
\(372\) −1.17535 −0.0609392
\(373\) −13.1037 −0.678486 −0.339243 0.940699i \(-0.610171\pi\)
−0.339243 + 0.940699i \(0.610171\pi\)
\(374\) −0.101500 −0.00524843
\(375\) 1.37625 0.0710692
\(376\) −63.8706 −3.29387
\(377\) −4.91770 −0.253275
\(378\) 13.4822 0.693449
\(379\) −0.966986 −0.0496707 −0.0248354 0.999692i \(-0.507906\pi\)
−0.0248354 + 0.999692i \(0.507906\pi\)
\(380\) 103.145 5.29125
\(381\) 2.46680 0.126378
\(382\) −10.4565 −0.535002
\(383\) −22.6049 −1.15506 −0.577529 0.816370i \(-0.695983\pi\)
−0.577529 + 0.816370i \(0.695983\pi\)
\(384\) 5.95406 0.303842
\(385\) −13.4649 −0.686233
\(386\) −10.3845 −0.528557
\(387\) −15.5447 −0.790181
\(388\) 55.9237 2.83910
\(389\) −27.3335 −1.38586 −0.692931 0.721004i \(-0.743681\pi\)
−0.692931 + 0.721004i \(0.743681\pi\)
\(390\) −6.49282 −0.328777
\(391\) −0.130227 −0.00658587
\(392\) −193.617 −9.77914
\(393\) 0.816318 0.0411778
\(394\) −40.5909 −2.04494
\(395\) −6.12611 −0.308238
\(396\) −16.2537 −0.816778
\(397\) 24.8277 1.24606 0.623032 0.782196i \(-0.285901\pi\)
0.623032 + 0.782196i \(0.285901\pi\)
\(398\) 64.2747 3.22180
\(399\) 6.06943 0.303852
\(400\) 23.8889 1.19445
\(401\) −24.6724 −1.23208 −0.616040 0.787715i \(-0.711264\pi\)
−0.616040 + 0.787715i \(0.711264\pi\)
\(402\) 3.79376 0.189216
\(403\) −8.01256 −0.399134
\(404\) −7.78413 −0.387275
\(405\) 22.5507 1.12056
\(406\) 11.9953 0.595316
\(407\) 5.04931 0.250285
\(408\) 0.0553978 0.00274260
\(409\) −5.03835 −0.249130 −0.124565 0.992211i \(-0.539754\pi\)
−0.124565 + 0.992211i \(0.539754\pi\)
\(410\) 20.7497 1.02475
\(411\) 1.90277 0.0938566
\(412\) −55.1530 −2.71719
\(413\) −35.5218 −1.74791
\(414\) −28.4884 −1.40013
\(415\) 17.7983 0.873685
\(416\) 128.170 6.28405
\(417\) −3.27005 −0.160135
\(418\) −20.0751 −0.981906
\(419\) −11.0465 −0.539654 −0.269827 0.962909i \(-0.586967\pi\)
−0.269827 + 0.962909i \(0.586967\pi\)
\(420\) 11.5932 0.565689
\(421\) 27.4976 1.34015 0.670076 0.742293i \(-0.266262\pi\)
0.670076 + 0.742293i \(0.266262\pi\)
\(422\) 13.6682 0.665359
\(423\) −20.0855 −0.976591
\(424\) −45.7886 −2.22369
\(425\) 0.0594904 0.00288571
\(426\) −4.40587 −0.213465
\(427\) 21.8015 1.05505
\(428\) 52.2145 2.52388
\(429\) 0.925043 0.0446615
\(430\) −36.6727 −1.76851
\(431\) −22.5048 −1.08402 −0.542010 0.840372i \(-0.682337\pi\)
−0.542010 + 0.840372i \(0.682337\pi\)
\(432\) 14.0496 0.675960
\(433\) 27.9936 1.34529 0.672644 0.739966i \(-0.265159\pi\)
0.672644 + 0.739966i \(0.265159\pi\)
\(434\) 19.5443 0.938155
\(435\) −0.339257 −0.0162661
\(436\) 12.9096 0.618259
\(437\) −25.7570 −1.23212
\(438\) 0.413327 0.0197495
\(439\) 5.00556 0.238902 0.119451 0.992840i \(-0.461887\pi\)
0.119451 + 0.992840i \(0.461887\pi\)
\(440\) −24.3075 −1.15881
\(441\) −60.8872 −2.89939
\(442\) 0.595755 0.0283372
\(443\) −3.95941 −0.188117 −0.0940587 0.995567i \(-0.529984\pi\)
−0.0940587 + 0.995567i \(0.529984\pi\)
\(444\) −4.34743 −0.206320
\(445\) 8.46977 0.401506
\(446\) 72.0626 3.41226
\(447\) 0.884554 0.0418380
\(448\) −156.255 −7.38236
\(449\) 33.9166 1.60063 0.800313 0.599583i \(-0.204667\pi\)
0.800313 + 0.599583i \(0.204667\pi\)
\(450\) 13.0141 0.613489
\(451\) −2.95624 −0.139204
\(452\) −64.0686 −3.01353
\(453\) 0.929368 0.0436655
\(454\) 72.5043 3.40280
\(455\) 79.0324 3.70510
\(456\) 10.9568 0.513101
\(457\) −23.3153 −1.09064 −0.545321 0.838227i \(-0.683592\pi\)
−0.545321 + 0.838227i \(0.683592\pi\)
\(458\) −32.4253 −1.51514
\(459\) 0.0349875 0.00163308
\(460\) −49.1982 −2.29388
\(461\) −26.9218 −1.25387 −0.626936 0.779070i \(-0.715691\pi\)
−0.626936 + 0.779070i \(0.715691\pi\)
\(462\) −2.25637 −0.104976
\(463\) −19.1265 −0.888886 −0.444443 0.895807i \(-0.646598\pi\)
−0.444443 + 0.895807i \(0.646598\pi\)
\(464\) 12.5001 0.580302
\(465\) −0.552762 −0.0256337
\(466\) −3.51756 −0.162948
\(467\) 34.4993 1.59644 0.798220 0.602367i \(-0.205775\pi\)
0.798220 + 0.602367i \(0.205775\pi\)
\(468\) 95.4014 4.40993
\(469\) −46.1787 −2.13233
\(470\) −47.3853 −2.18572
\(471\) 3.79086 0.174674
\(472\) −64.1257 −2.95163
\(473\) 5.22482 0.240237
\(474\) −1.02658 −0.0471524
\(475\) 11.7663 0.539875
\(476\) −1.06374 −0.0487566
\(477\) −14.3992 −0.659296
\(478\) 56.5707 2.58749
\(479\) 19.2630 0.880151 0.440076 0.897961i \(-0.354952\pi\)
0.440076 + 0.897961i \(0.354952\pi\)
\(480\) 8.84206 0.403583
\(481\) −29.6371 −1.35133
\(482\) 34.5890 1.57549
\(483\) −2.89499 −0.131727
\(484\) 5.46313 0.248324
\(485\) 26.3006 1.19425
\(486\) 11.4967 0.521500
\(487\) −1.31178 −0.0594424 −0.0297212 0.999558i \(-0.509462\pi\)
−0.0297212 + 0.999558i \(0.509462\pi\)
\(488\) 39.3571 1.78161
\(489\) 2.60102 0.117622
\(490\) −143.644 −6.48916
\(491\) 39.3594 1.77627 0.888133 0.459586i \(-0.152002\pi\)
0.888133 + 0.459586i \(0.152002\pi\)
\(492\) 2.54531 0.114751
\(493\) 0.0311289 0.00140198
\(494\) 117.831 5.30149
\(495\) −7.64402 −0.343573
\(496\) 20.3668 0.914495
\(497\) 53.6295 2.40561
\(498\) 2.98255 0.133651
\(499\) −11.5307 −0.516185 −0.258092 0.966120i \(-0.583094\pi\)
−0.258092 + 0.966120i \(0.583094\pi\)
\(500\) −47.7067 −2.13351
\(501\) 2.21305 0.0988720
\(502\) −29.6094 −1.32153
\(503\) 34.0563 1.51849 0.759247 0.650802i \(-0.225567\pi\)
0.759247 + 0.650802i \(0.225567\pi\)
\(504\) −147.513 −6.57075
\(505\) −3.66083 −0.162905
\(506\) 9.57541 0.425679
\(507\) −3.38075 −0.150145
\(508\) −85.5099 −3.79389
\(509\) 31.6683 1.40367 0.701837 0.712338i \(-0.252364\pi\)
0.701837 + 0.712338i \(0.252364\pi\)
\(510\) 0.0410994 0.00181991
\(511\) −5.03113 −0.222564
\(512\) −43.4885 −1.92194
\(513\) 6.92001 0.305526
\(514\) −74.1941 −3.27256
\(515\) −25.9381 −1.14297
\(516\) −4.49854 −0.198037
\(517\) 6.75107 0.296912
\(518\) 72.2909 3.17628
\(519\) −3.58477 −0.157354
\(520\) 142.673 6.25664
\(521\) 15.5890 0.682966 0.341483 0.939888i \(-0.389071\pi\)
0.341483 + 0.939888i \(0.389071\pi\)
\(522\) 6.80974 0.298054
\(523\) 28.4761 1.24517 0.622587 0.782550i \(-0.286082\pi\)
0.622587 + 0.782550i \(0.286082\pi\)
\(524\) −28.2971 −1.23616
\(525\) 1.32249 0.0577182
\(526\) −64.1273 −2.79608
\(527\) 0.0507192 0.00220936
\(528\) −2.35133 −0.102328
\(529\) −10.7145 −0.465847
\(530\) −33.9704 −1.47558
\(531\) −20.1658 −0.875119
\(532\) −210.392 −9.12167
\(533\) 17.3517 0.751587
\(534\) 1.41932 0.0614199
\(535\) 24.5562 1.06166
\(536\) −83.3641 −3.60078
\(537\) 1.24590 0.0537644
\(538\) −40.9889 −1.76716
\(539\) 20.4652 0.881497
\(540\) 13.2179 0.568806
\(541\) 30.6768 1.31890 0.659448 0.751750i \(-0.270790\pi\)
0.659448 + 0.751750i \(0.270790\pi\)
\(542\) 30.5975 1.31428
\(543\) 3.84644 0.165066
\(544\) −0.811312 −0.0347847
\(545\) 6.07133 0.260067
\(546\) 13.2438 0.566784
\(547\) 1.00000 0.0427569
\(548\) −65.9580 −2.81759
\(549\) 12.3767 0.528225
\(550\) −4.37424 −0.186518
\(551\) 6.15683 0.262290
\(552\) −5.22618 −0.222441
\(553\) 12.4958 0.531377
\(554\) 71.4834 3.03704
\(555\) −2.04457 −0.0867872
\(556\) 113.354 4.80728
\(557\) −16.9107 −0.716530 −0.358265 0.933620i \(-0.616632\pi\)
−0.358265 + 0.933620i \(0.616632\pi\)
\(558\) 11.0953 0.469701
\(559\) −30.6672 −1.29708
\(560\) −200.889 −8.48911
\(561\) −0.00585550 −0.000247219 0
\(562\) −71.7376 −3.02607
\(563\) −14.4225 −0.607837 −0.303919 0.952698i \(-0.598295\pi\)
−0.303919 + 0.952698i \(0.598295\pi\)
\(564\) −5.81263 −0.244756
\(565\) −30.1311 −1.26763
\(566\) 67.0089 2.81659
\(567\) −45.9982 −1.93174
\(568\) 96.8147 4.06225
\(569\) −34.7394 −1.45635 −0.728175 0.685391i \(-0.759631\pi\)
−0.728175 + 0.685391i \(0.759631\pi\)
\(570\) 8.12883 0.340479
\(571\) 11.4336 0.478481 0.239241 0.970960i \(-0.423102\pi\)
0.239241 + 0.970960i \(0.423102\pi\)
\(572\) −32.0660 −1.34075
\(573\) −0.603234 −0.0252005
\(574\) −42.3245 −1.76659
\(575\) −5.61228 −0.234048
\(576\) −88.7061 −3.69609
\(577\) 3.65403 0.152119 0.0760596 0.997103i \(-0.475766\pi\)
0.0760596 + 0.997103i \(0.475766\pi\)
\(578\) 46.4381 1.93157
\(579\) −0.599080 −0.0248969
\(580\) 11.7601 0.488312
\(581\) −36.3044 −1.50616
\(582\) 4.40731 0.182689
\(583\) 4.83982 0.200445
\(584\) −9.08245 −0.375834
\(585\) 44.8668 1.85501
\(586\) −64.5730 −2.66749
\(587\) −20.4690 −0.844844 −0.422422 0.906399i \(-0.638820\pi\)
−0.422422 + 0.906399i \(0.638820\pi\)
\(588\) −17.6204 −0.726652
\(589\) 10.0315 0.413341
\(590\) −47.5746 −1.95862
\(591\) −2.34168 −0.0963237
\(592\) 75.3332 3.09617
\(593\) −12.8228 −0.526571 −0.263285 0.964718i \(-0.584806\pi\)
−0.263285 + 0.964718i \(0.584806\pi\)
\(594\) −2.57258 −0.105554
\(595\) −0.500273 −0.0205092
\(596\) −30.6624 −1.25598
\(597\) 3.70799 0.151758
\(598\) −56.2031 −2.29832
\(599\) −16.8927 −0.690217 −0.345108 0.938563i \(-0.612158\pi\)
−0.345108 + 0.938563i \(0.612158\pi\)
\(600\) 2.38743 0.0974663
\(601\) 34.0593 1.38931 0.694655 0.719343i \(-0.255557\pi\)
0.694655 + 0.719343i \(0.255557\pi\)
\(602\) 74.8036 3.04877
\(603\) −26.2157 −1.06759
\(604\) −32.2159 −1.31084
\(605\) 2.56928 0.104456
\(606\) −0.613463 −0.0249202
\(607\) −11.2167 −0.455274 −0.227637 0.973746i \(-0.573100\pi\)
−0.227637 + 0.973746i \(0.573100\pi\)
\(608\) −160.465 −6.50772
\(609\) 0.692005 0.0280415
\(610\) 29.1989 1.18223
\(611\) −39.6256 −1.60308
\(612\) −0.603888 −0.0244107
\(613\) 10.4189 0.420815 0.210408 0.977614i \(-0.432521\pi\)
0.210408 + 0.977614i \(0.432521\pi\)
\(614\) −46.9037 −1.89288
\(615\) 1.19704 0.0482695
\(616\) 49.5815 1.99770
\(617\) 25.1418 1.01217 0.506086 0.862483i \(-0.331092\pi\)
0.506086 + 0.862483i \(0.331092\pi\)
\(618\) −4.34658 −0.174845
\(619\) −5.44850 −0.218994 −0.109497 0.993987i \(-0.534924\pi\)
−0.109497 + 0.993987i \(0.534924\pi\)
\(620\) 19.1611 0.769528
\(621\) −3.30070 −0.132452
\(622\) 50.6241 2.02984
\(623\) −17.2763 −0.692162
\(624\) 13.8012 0.552489
\(625\) −30.4421 −1.21769
\(626\) 66.2297 2.64707
\(627\) −1.15813 −0.0462512
\(628\) −131.407 −5.24372
\(629\) 0.187602 0.00748017
\(630\) −109.439 −4.36016
\(631\) 2.32525 0.0925669 0.0462834 0.998928i \(-0.485262\pi\)
0.0462834 + 0.998928i \(0.485262\pi\)
\(632\) 22.5581 0.897313
\(633\) 0.788517 0.0313407
\(634\) 0.493247 0.0195893
\(635\) −40.2148 −1.59588
\(636\) −4.16706 −0.165235
\(637\) −120.121 −4.75936
\(638\) −2.28886 −0.0906169
\(639\) 30.4455 1.20441
\(640\) −97.0655 −3.83685
\(641\) 46.3201 1.82953 0.914767 0.403981i \(-0.132374\pi\)
0.914767 + 0.403981i \(0.132374\pi\)
\(642\) 4.11500 0.162406
\(643\) −12.6051 −0.497096 −0.248548 0.968620i \(-0.579953\pi\)
−0.248548 + 0.968620i \(0.579953\pi\)
\(644\) 100.353 3.95445
\(645\) −2.11564 −0.0833032
\(646\) −0.745869 −0.0293458
\(647\) 28.4620 1.11896 0.559479 0.828845i \(-0.311001\pi\)
0.559479 + 0.828845i \(0.311001\pi\)
\(648\) −83.0383 −3.26205
\(649\) 6.77803 0.266061
\(650\) 25.6747 1.00705
\(651\) 1.12750 0.0441904
\(652\) −90.1626 −3.53104
\(653\) 26.7712 1.04764 0.523819 0.851830i \(-0.324507\pi\)
0.523819 + 0.851830i \(0.324507\pi\)
\(654\) 1.01740 0.0397835
\(655\) −13.3080 −0.519985
\(656\) −44.1056 −1.72204
\(657\) −2.85618 −0.111430
\(658\) 96.6549 3.76800
\(659\) −19.2650 −0.750460 −0.375230 0.926932i \(-0.622436\pi\)
−0.375230 + 0.926932i \(0.622436\pi\)
\(660\) −2.21213 −0.0861072
\(661\) −23.7344 −0.923161 −0.461580 0.887098i \(-0.652717\pi\)
−0.461580 + 0.887098i \(0.652717\pi\)
\(662\) −5.69205 −0.221228
\(663\) 0.0343690 0.00133478
\(664\) −65.5385 −2.54339
\(665\) −98.9464 −3.83698
\(666\) 41.0396 1.59025
\(667\) −2.93668 −0.113709
\(668\) −76.7139 −2.96815
\(669\) 4.15727 0.160730
\(670\) −61.8475 −2.38938
\(671\) −4.16001 −0.160595
\(672\) −18.0357 −0.695743
\(673\) −11.4270 −0.440477 −0.220239 0.975446i \(-0.570684\pi\)
−0.220239 + 0.975446i \(0.570684\pi\)
\(674\) −15.5934 −0.600635
\(675\) 1.50783 0.0580362
\(676\) 117.191 4.50736
\(677\) 7.14029 0.274424 0.137212 0.990542i \(-0.456186\pi\)
0.137212 + 0.990542i \(0.456186\pi\)
\(678\) −5.04921 −0.193914
\(679\) −53.6470 −2.05878
\(680\) −0.903118 −0.0346330
\(681\) 4.18276 0.160284
\(682\) −3.72931 −0.142803
\(683\) 23.2320 0.888946 0.444473 0.895792i \(-0.353391\pi\)
0.444473 + 0.895792i \(0.353391\pi\)
\(684\) −119.440 −4.56690
\(685\) −31.0197 −1.18520
\(686\) 192.780 7.36039
\(687\) −1.87061 −0.0713682
\(688\) 77.9516 2.97188
\(689\) −28.4074 −1.08224
\(690\) −3.87728 −0.147606
\(691\) −42.1437 −1.60322 −0.801612 0.597845i \(-0.796024\pi\)
−0.801612 + 0.597845i \(0.796024\pi\)
\(692\) 124.264 4.72379
\(693\) 15.5920 0.592291
\(694\) 79.8816 3.03226
\(695\) 53.3098 2.02215
\(696\) 1.24924 0.0473524
\(697\) −0.109836 −0.00416034
\(698\) 14.5954 0.552443
\(699\) −0.202927 −0.00767542
\(700\) −45.8432 −1.73271
\(701\) −20.0383 −0.756837 −0.378419 0.925635i \(-0.623532\pi\)
−0.378419 + 0.925635i \(0.623532\pi\)
\(702\) 15.0998 0.569906
\(703\) 37.1048 1.39943
\(704\) 29.8156 1.12372
\(705\) −2.73365 −0.102955
\(706\) 42.9423 1.61615
\(707\) 7.46723 0.280834
\(708\) −5.83585 −0.219325
\(709\) 18.4645 0.693449 0.346724 0.937967i \(-0.387294\pi\)
0.346724 + 0.937967i \(0.387294\pi\)
\(710\) 71.8264 2.69560
\(711\) 7.09389 0.266042
\(712\) −31.1881 −1.16882
\(713\) −4.78481 −0.179193
\(714\) −0.0838330 −0.00313737
\(715\) −15.0804 −0.563977
\(716\) −43.1881 −1.61402
\(717\) 3.26355 0.121880
\(718\) 0.937179 0.0349752
\(719\) −33.9169 −1.26489 −0.632444 0.774606i \(-0.717948\pi\)
−0.632444 + 0.774606i \(0.717948\pi\)
\(720\) −114.045 −4.25020
\(721\) 52.9077 1.97039
\(722\) −95.6161 −3.55846
\(723\) 1.99543 0.0742109
\(724\) −133.334 −4.95532
\(725\) 1.34153 0.0498233
\(726\) 0.430546 0.0159791
\(727\) −0.642922 −0.0238447 −0.0119223 0.999929i \(-0.503795\pi\)
−0.0119223 + 0.999929i \(0.503795\pi\)
\(728\) −291.020 −10.7859
\(729\) −25.6680 −0.950666
\(730\) −6.73823 −0.249393
\(731\) 0.194122 0.00717988
\(732\) 3.58174 0.132385
\(733\) 9.28785 0.343055 0.171527 0.985179i \(-0.445130\pi\)
0.171527 + 0.985179i \(0.445130\pi\)
\(734\) −54.7287 −2.02007
\(735\) −8.28677 −0.305662
\(736\) 76.5385 2.82125
\(737\) 8.81152 0.324576
\(738\) −24.0276 −0.884470
\(739\) −4.98727 −0.183460 −0.0917298 0.995784i \(-0.529240\pi\)
−0.0917298 + 0.995784i \(0.529240\pi\)
\(740\) 70.8736 2.60537
\(741\) 6.79767 0.249719
\(742\) 69.2916 2.54377
\(743\) −6.16632 −0.226220 −0.113110 0.993582i \(-0.536081\pi\)
−0.113110 + 0.993582i \(0.536081\pi\)
\(744\) 2.03543 0.0746224
\(745\) −14.4204 −0.528322
\(746\) 35.7977 1.31065
\(747\) −20.6100 −0.754081
\(748\) 0.202977 0.00742156
\(749\) −50.0889 −1.83021
\(750\) −3.75974 −0.137286
\(751\) 7.36737 0.268839 0.134420 0.990925i \(-0.457083\pi\)
0.134420 + 0.990925i \(0.457083\pi\)
\(752\) 100.722 3.67297
\(753\) −1.70816 −0.0622488
\(754\) 13.4345 0.489257
\(755\) −15.1509 −0.551399
\(756\) −26.9613 −0.980573
\(757\) −15.0272 −0.546173 −0.273086 0.961990i \(-0.588044\pi\)
−0.273086 + 0.961990i \(0.588044\pi\)
\(758\) 2.64168 0.0959502
\(759\) 0.552403 0.0200510
\(760\) −178.623 −6.47934
\(761\) −21.7547 −0.788609 −0.394304 0.918980i \(-0.629014\pi\)
−0.394304 + 0.918980i \(0.629014\pi\)
\(762\) −6.73898 −0.244128
\(763\) −12.3841 −0.448334
\(764\) 20.9107 0.756521
\(765\) −0.284005 −0.0102682
\(766\) 61.7538 2.23126
\(767\) −39.7839 −1.43651
\(768\) −6.86780 −0.247820
\(769\) −4.92494 −0.177598 −0.0887989 0.996050i \(-0.528303\pi\)
−0.0887989 + 0.996050i \(0.528303\pi\)
\(770\) 36.7843 1.32561
\(771\) −4.28024 −0.154149
\(772\) 20.7667 0.747408
\(773\) 9.65747 0.347355 0.173678 0.984803i \(-0.444435\pi\)
0.173678 + 0.984803i \(0.444435\pi\)
\(774\) 42.4661 1.52641
\(775\) 2.18580 0.0785163
\(776\) −96.8464 −3.47658
\(777\) 4.17044 0.149614
\(778\) 74.6716 2.67711
\(779\) −21.7239 −0.778340
\(780\) 12.9842 0.464908
\(781\) −10.2332 −0.366174
\(782\) 0.355764 0.0127221
\(783\) 0.788984 0.0281960
\(784\) 305.330 10.9046
\(785\) −61.8002 −2.20574
\(786\) −2.23008 −0.0795442
\(787\) 29.0273 1.03471 0.517355 0.855771i \(-0.326917\pi\)
0.517355 + 0.855771i \(0.326917\pi\)
\(788\) 81.1725 2.89165
\(789\) −3.69949 −0.131705
\(790\) 16.7358 0.595431
\(791\) 61.4604 2.18528
\(792\) 28.1475 1.00018
\(793\) 24.4173 0.867083
\(794\) −67.8260 −2.40705
\(795\) −1.95974 −0.0695049
\(796\) −128.535 −4.55579
\(797\) 52.2291 1.85005 0.925025 0.379905i \(-0.124043\pi\)
0.925025 + 0.379905i \(0.124043\pi\)
\(798\) −16.5809 −0.586958
\(799\) 0.250829 0.00887368
\(800\) −34.9644 −1.23618
\(801\) −9.80779 −0.346541
\(802\) 67.4018 2.38004
\(803\) 0.960007 0.0338779
\(804\) −7.58666 −0.267561
\(805\) 47.1953 1.66342
\(806\) 21.8893 0.771017
\(807\) −2.36464 −0.0832392
\(808\) 13.4802 0.474233
\(809\) 51.7190 1.81834 0.909171 0.416423i \(-0.136717\pi\)
0.909171 + 0.416423i \(0.136717\pi\)
\(810\) −61.6057 −2.16461
\(811\) −29.4723 −1.03491 −0.517456 0.855710i \(-0.673121\pi\)
−0.517456 + 0.855710i \(0.673121\pi\)
\(812\) −23.9879 −0.841809
\(813\) 1.76516 0.0619069
\(814\) −13.7941 −0.483482
\(815\) −42.4030 −1.48531
\(816\) −0.0873610 −0.00305825
\(817\) 38.3945 1.34325
\(818\) 13.7641 0.481252
\(819\) −91.5176 −3.19788
\(820\) −41.4947 −1.44906
\(821\) 7.21594 0.251838 0.125919 0.992041i \(-0.459812\pi\)
0.125919 + 0.992041i \(0.459812\pi\)
\(822\) −5.19811 −0.181305
\(823\) 37.0057 1.28994 0.644970 0.764208i \(-0.276870\pi\)
0.644970 + 0.764208i \(0.276870\pi\)
\(824\) 95.5117 3.32731
\(825\) −0.252349 −0.00878566
\(826\) 97.0410 3.37649
\(827\) 0.602123 0.0209379 0.0104689 0.999945i \(-0.496668\pi\)
0.0104689 + 0.999945i \(0.496668\pi\)
\(828\) 56.9703 1.97986
\(829\) 1.43310 0.0497735 0.0248867 0.999690i \(-0.492077\pi\)
0.0248867 + 0.999690i \(0.492077\pi\)
\(830\) −48.6227 −1.68772
\(831\) 4.12386 0.143055
\(832\) −175.003 −6.06715
\(833\) 0.760361 0.0263449
\(834\) 8.93336 0.309337
\(835\) −36.0781 −1.24854
\(836\) 40.1457 1.38847
\(837\) 1.28551 0.0444339
\(838\) 30.1775 1.04246
\(839\) −25.2488 −0.871687 −0.435843 0.900023i \(-0.643550\pi\)
−0.435843 + 0.900023i \(0.643550\pi\)
\(840\) −20.0766 −0.692708
\(841\) −28.2980 −0.975794
\(842\) −75.1199 −2.58880
\(843\) −4.13852 −0.142538
\(844\) −27.3334 −0.940854
\(845\) 55.1144 1.89599
\(846\) 54.8711 1.88651
\(847\) −5.24072 −0.180073
\(848\) 72.2076 2.47962
\(849\) 3.86573 0.132671
\(850\) −0.162520 −0.00557440
\(851\) −17.6982 −0.606686
\(852\) 8.81075 0.301851
\(853\) −9.91043 −0.339327 −0.169663 0.985502i \(-0.554268\pi\)
−0.169663 + 0.985502i \(0.554268\pi\)
\(854\) −59.5588 −2.03806
\(855\) −56.1719 −1.92104
\(856\) −90.4229 −3.09059
\(857\) −45.4206 −1.55154 −0.775770 0.631016i \(-0.782638\pi\)
−0.775770 + 0.631016i \(0.782638\pi\)
\(858\) −2.52710 −0.0862738
\(859\) −8.84740 −0.301869 −0.150935 0.988544i \(-0.548228\pi\)
−0.150935 + 0.988544i \(0.548228\pi\)
\(860\) 73.3371 2.50077
\(861\) −2.44169 −0.0832125
\(862\) 61.4804 2.09403
\(863\) 20.6639 0.703406 0.351703 0.936112i \(-0.385603\pi\)
0.351703 + 0.936112i \(0.385603\pi\)
\(864\) −20.5633 −0.699576
\(865\) 58.4405 1.98704
\(866\) −76.4750 −2.59873
\(867\) 2.67900 0.0909836
\(868\) −39.0841 −1.32660
\(869\) −2.38437 −0.0808842
\(870\) 0.926808 0.0314217
\(871\) −51.7194 −1.75245
\(872\) −22.3564 −0.757082
\(873\) −30.4555 −1.03076
\(874\) 70.3647 2.38012
\(875\) 45.7646 1.54712
\(876\) −0.826560 −0.0279269
\(877\) 25.0428 0.845636 0.422818 0.906215i \(-0.361041\pi\)
0.422818 + 0.906215i \(0.361041\pi\)
\(878\) −13.6745 −0.461493
\(879\) −3.72520 −0.125648
\(880\) 38.3323 1.29218
\(881\) −4.69467 −0.158168 −0.0790838 0.996868i \(-0.525199\pi\)
−0.0790838 + 0.996868i \(0.525199\pi\)
\(882\) 166.336 5.60082
\(883\) −30.6830 −1.03257 −0.516283 0.856418i \(-0.672685\pi\)
−0.516283 + 0.856418i \(0.672685\pi\)
\(884\) −1.19138 −0.0400703
\(885\) −2.74457 −0.0922576
\(886\) 10.8166 0.363391
\(887\) −32.2433 −1.08262 −0.541312 0.840822i \(-0.682072\pi\)
−0.541312 + 0.840822i \(0.682072\pi\)
\(888\) 7.52870 0.252647
\(889\) 82.0287 2.75116
\(890\) −23.1383 −0.775598
\(891\) 8.77707 0.294043
\(892\) −144.109 −4.82512
\(893\) 49.6101 1.66014
\(894\) −2.41649 −0.0808195
\(895\) −20.3111 −0.678926
\(896\) 197.991 6.61441
\(897\) −3.24234 −0.108259
\(898\) −92.6559 −3.09197
\(899\) 1.14374 0.0381459
\(900\) −26.0252 −0.867507
\(901\) 0.179818 0.00599061
\(902\) 8.07608 0.268904
\(903\) 4.31540 0.143608
\(904\) 110.951 3.69019
\(905\) −62.7062 −2.08443
\(906\) −2.53891 −0.0843498
\(907\) 1.51259 0.0502248 0.0251124 0.999685i \(-0.492006\pi\)
0.0251124 + 0.999685i \(0.492006\pi\)
\(908\) −144.992 −4.81174
\(909\) 4.23916 0.140604
\(910\) −215.906 −7.15723
\(911\) −19.5471 −0.647623 −0.323811 0.946122i \(-0.604964\pi\)
−0.323811 + 0.946122i \(0.604964\pi\)
\(912\) −17.2787 −0.572155
\(913\) 6.92736 0.229262
\(914\) 63.6943 2.10682
\(915\) 1.68447 0.0556870
\(916\) 64.8433 2.14248
\(917\) 27.1451 0.896410
\(918\) −0.0955815 −0.00315466
\(919\) 53.9399 1.77931 0.889657 0.456629i \(-0.150943\pi\)
0.889657 + 0.456629i \(0.150943\pi\)
\(920\) 85.1994 2.80894
\(921\) −2.70586 −0.0891612
\(922\) 73.5469 2.42214
\(923\) 60.0642 1.97704
\(924\) 4.51223 0.148441
\(925\) 8.08490 0.265830
\(926\) 52.2513 1.71708
\(927\) 30.0357 0.986503
\(928\) −18.2954 −0.600577
\(929\) 4.12701 0.135403 0.0677014 0.997706i \(-0.478433\pi\)
0.0677014 + 0.997706i \(0.478433\pi\)
\(930\) 1.51007 0.0495173
\(931\) 150.388 4.92876
\(932\) 7.03433 0.230417
\(933\) 2.92049 0.0956125
\(934\) −94.2478 −3.08388
\(935\) 0.0954587 0.00312183
\(936\) −165.212 −5.40013
\(937\) 29.5399 0.965026 0.482513 0.875889i \(-0.339724\pi\)
0.482513 + 0.875889i \(0.339724\pi\)
\(938\) 126.154 4.11908
\(939\) 3.82077 0.124686
\(940\) 94.7599 3.09073
\(941\) −23.5330 −0.767154 −0.383577 0.923509i \(-0.625308\pi\)
−0.383577 + 0.923509i \(0.625308\pi\)
\(942\) −10.3561 −0.337421
\(943\) 10.3618 0.337428
\(944\) 101.125 3.29133
\(945\) −12.6798 −0.412472
\(946\) −14.2735 −0.464073
\(947\) −1.06140 −0.0344909 −0.0172454 0.999851i \(-0.505490\pi\)
−0.0172454 + 0.999851i \(0.505490\pi\)
\(948\) 2.05293 0.0666761
\(949\) −5.63479 −0.182913
\(950\) −32.1440 −1.04289
\(951\) 0.0284553 0.000922727 0
\(952\) 1.84215 0.0597043
\(953\) 60.4873 1.95938 0.979688 0.200526i \(-0.0642651\pi\)
0.979688 + 0.200526i \(0.0642651\pi\)
\(954\) 39.3369 1.27358
\(955\) 9.83417 0.318226
\(956\) −113.129 −3.65884
\(957\) −0.132044 −0.00426837
\(958\) −52.6242 −1.70021
\(959\) 63.2729 2.04319
\(960\) −12.0729 −0.389653
\(961\) −29.1365 −0.939886
\(962\) 80.9647 2.61041
\(963\) −28.4355 −0.916321
\(964\) −69.1701 −2.22782
\(965\) 9.76644 0.314393
\(966\) 7.90874 0.254460
\(967\) −28.4188 −0.913888 −0.456944 0.889496i \(-0.651056\pi\)
−0.456944 + 0.889496i \(0.651056\pi\)
\(968\) −9.46082 −0.304082
\(969\) −0.0430290 −0.00138229
\(970\) −71.8499 −2.30696
\(971\) 56.2449 1.80498 0.902492 0.430706i \(-0.141735\pi\)
0.902492 + 0.430706i \(0.141735\pi\)
\(972\) −22.9907 −0.737429
\(973\) −108.739 −3.48602
\(974\) 3.58361 0.114826
\(975\) 1.48117 0.0474354
\(976\) −62.0652 −1.98666
\(977\) −37.2944 −1.19315 −0.596576 0.802556i \(-0.703473\pi\)
−0.596576 + 0.802556i \(0.703473\pi\)
\(978\) −7.10567 −0.227214
\(979\) 3.29656 0.105358
\(980\) 287.255 9.17602
\(981\) −7.03045 −0.224465
\(982\) −107.525 −3.43126
\(983\) 20.3664 0.649587 0.324794 0.945785i \(-0.394705\pi\)
0.324794 + 0.945785i \(0.394705\pi\)
\(984\) −4.40786 −0.140517
\(985\) 38.1750 1.21636
\(986\) −0.0850402 −0.00270823
\(987\) 5.57600 0.177486
\(988\) −235.636 −7.49659
\(989\) −18.3134 −0.582331
\(990\) 20.8825 0.663689
\(991\) 4.30846 0.136863 0.0684313 0.997656i \(-0.478201\pi\)
0.0684313 + 0.997656i \(0.478201\pi\)
\(992\) −29.8093 −0.946445
\(993\) −0.328373 −0.0104206
\(994\) −146.509 −4.64698
\(995\) −60.4492 −1.91637
\(996\) −5.96442 −0.188990
\(997\) 56.3954 1.78606 0.893030 0.449997i \(-0.148575\pi\)
0.893030 + 0.449997i \(0.148575\pi\)
\(998\) 31.5004 0.997127
\(999\) 4.75490 0.150438
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))